We present the results of 16 years of monitoring stellar orbits around the massive black hole in center of the Milky Way using high resolution NIR techniques. This work refines our previous analysis mainly by greatly improving the definition of the coordinate system, which reaches a long-term astrometric accuracy of 300 microarcsecond, and by investigating in detail the individual systematic error contributions. The combination of a long time baseline and the excellent astrometric accuracy of adaptive optics data allow us to determine orbits of 28 stars, including the star S2, which has completed a full revolution since our monitoring began. Our main results are: all stellar orbits are fit extremely well by a single point mass potential to within the astrometric uncertainties, which are now 6 times better than in previous studies. The central object mass is (4.31 +- 0.06|stat +- 0.36|R0) * 10^6 M_sun where the fractional statistical error of 1.5 percent is nearly independent from R0 and the main uncertainty is due to the uncertainty in R0. Our current best estimate for the distance to the Galactic Center is R0 = 8.33 +- 0.35 kpc. The dominant errors in this value is systematic. The mass scales with distance as (3.95 +- 0.06) * 10^6 M_sun * (R0/8kpc)^2.19. The orientations of orbital angular momenta for stars in the central arcsecond are random. We identify six of the stars with orbital solutions as late type stars, and six early-type stars as members of the clockwise rotating disk system, as was previously proposed. We constrain the extended dark mass enclosed between the pericenter and apocenter of S2 at less than 0.066, at the 99% confidence level, of the mass of Sgr A*. This is two orders of magnitudes larger than what one would expect from other theoretical and observational estimates.
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